Abstract

This lesson is designed to familiarize students to the Cartesian Coordinate System and its many uses in the world of mathematics. The Cartesian coordinate system was developed by the mathematician Descartes during an illness. As he lay in bed sick, he saw a fly buzzing around on the ceiling, which was made of square tiles. As he watched he realized that he could describe the position of the fly by the ceiling tile he was on. After this experience he developed the coordinate plane to make it easier to describe the position of objects.

Objectives

Upon completion of this lesson, students will:

• have been introduced to the Cartesian coordinate plane
• be able to plot points on the plane
• be able to read coordinates for a point from a graph
• be able to give the ratio of rise over run for slope

Standards

The activities and discussions in this lesson address the following NCTM standards:

Algebra

Understand patterns, relationships and functions

• represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules;

• develop an initial conceptual understanding of different uses of variables;
• explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope;
• use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships;
• recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

• model and solve contextualized problems using various representations, such as graphs, tables, and equations

Student Prerequisites

• Arithmetic: Students must be able to:
  • perform integer and fractional arithmetic
• Algebraic: Students must be able to:
  • work with very simple linear algebraic expressions
• Technological Students must be able to:
  • perform basic mouse manipulations such as point, click and drag
  • use a browser such as Netscape for experimenting with the activities

Teacher Preparation

Students will need:

• Access to a browser
• pencil
• Copies of supplemental materials for the activities:
  • Coordinates Game Suggestions
  • Maze Game Suggestions

Key Terms

• coordinate
• coordinate plane
• function
• graph
• negative numbers

Lesson Outline

This lesson is best if the students work in small groups of two or three.

1. Focus and Review

   Remind students what has been learned in previous lessons that will be pertinent to this lesson and/or have them begin to think about the words and ideas of this lesson:

   • Choose a student in the class, ask another student to describe that persons location in the classroom. For example 3rd row 4th seat back. Use this as an application of the coordinate system.

2. Objectives

   Let the students know what it is they will be doing and learning today. Say something like this:

   • Today, class, we are going to learn about cartesian coordinate system.
   • We are going to use the computers to learn cartesian coordinate system, but please do not turn your computers on until I ask you to. I want to show you a little about this activity first.

3. Teacher Input

   • Begin this lesson with a discussion of the coordinate plane.

4. Guided Practice

   • Have students practice their skills with the General Coordinates Game.
   • For further practice or an alternative game, have the students play the Maze Game.

   • To show students that the coordinate plane is useful in more than just describing the location of objects lead a discussion on reading points off a graph. This will show the students that they can read graphs and find the equations of lines using their knowledge of the coordinate plane.

5. Independent Practice
   • Have the student graph functions and points using the Graphit Applet. Or split up the graphing by using the Simple Plot applet to graph points and the Graph Sketcher applet to graph functions.

6. Closure

   • You may wish to bring the class back together for a discussion of the findings. Once the students have been allowed to share what they found, summarize the results of the lesson.

Alternate Outlines

• Omit one or the other of the computer activities to reduce the amount of time spent.
• Add a discussion about fractional movement on the coordinate plane.
• For students who aren't ready to handle negative numbers yet, replace the Coordinates activity with the positive numbers only alternate versions:
  • Simple Coordinates!
    Coordinates Worksheet
  • Simple Maze Game
    Maze Game Worksheet

Suggested Follow-Up

After these discussions and activities, students will be have learned to plot points on the coordinate plane and to read the coordinates off of a graph. The next lesson Functions and Graphs will introduce students to the graphical representation of functions.